Sheppard Colin J R, Bendandi Artemi, Le Gratiet Aymeric, Diaspro Alberto
J Opt Soc Am A Opt Image Sci Vis. 2020 Jul 1;37(7):1143-1154. doi: 10.1364/JOSAA.391902.
Calculation of the eigenvectors of two- and three-dimensional coherency matrices, and the four-dimensional coherency matrix associated with a Mueller matrix, is considered, especially for algebraic cases, in the light of recently published algorithms. The preferred approach is based on a combination of an evaluation of the characteristic polynomial and an adjugate matrix. The diagonal terms of the coherency matrix are given in terms of the characteristic polynomial of reduced matrices as functions of the eigenvalues of the coherency matrix. The analogous polynomial form for the off-diagonal elements of the coherency matrix is also presented. Simple expressions are given for the pure component in the characteristic decomposition.
考虑了二维和三维相干矩阵以及与穆勒矩阵相关的四维相干矩阵的特征向量计算，特别是对于代数情形，根据最近发表的算法进行了研究。首选方法基于特征多项式求值和伴随矩阵的组合。相干矩阵的对角项根据简化矩阵的特征多项式给出，作为相干矩阵特征值的函数。还给出了相干矩阵非对角元素的类似多项式形式。给出了特征分解中纯分量的简单表达式。
